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Let ME M2x2 (R) be a given but arbitrary matrix. Define T : M2x2(R) + M2x2 (R) by T(A) = AM + MA for any

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Let ME M2x2 (R) be a given but arbitrary matrix. Define T : M2x2(R) + M2x2 (R) by T(A) = AM + MA for any A E M2x2 (R). Is T a linear transformation? If so, show that it is. If not, explain why not with a counterexample. Show all your work. It is not sufficient to simply write down the answer without calculations or reasons

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